In this paper we exploit the fact that dense granular flow down an inclined chute exhibits a simple scaling property. This implies that the fundamental governing partial differential equation admits similarity profiles which are applicable to any general friction law \(\mu (I)\) of the material irrespective of the particular functional form under consideration, where \(\mu (I)\) is a function of the dimensionless parameter, called the inertial number I. We adopt a widely accepted constitutive model describing the material response that draws its original inspiration from the realms of classical visco-plasticity. The governing steady-state similarity solutions are however applicable for any friction law describing dense granular media. These steady-state solutions embody the key aspects of dense granular flow down an inclined chute that find wide usage in various industrial applications and will further aid in modelling natural geophysical phenomenon. We provide steady-state analytical solutions for some special cases and we emphasize the importance of similarity solutions as a benchmark standard for various numerical studies concerning the complex material behaviour of dense granular flows.

在本文中，我们利用了一个事实，即顺着斜槽滑落的致密颗粒流显示出简单的缩放特性。这意味着基本的控制偏微分方程允许相似性分布，该相似性分布适用于材料的任何一般摩擦定律\（\ mu（I）\），而与所考虑的特定功能形式无关，其中\（\ mu（I）\ ）是无量纲参数的函数，称为惯性数I。我们采用了一种被广泛接受的本构模型，该模型描述了从经典粘塑性领域汲取其原始灵感的材料响应。但是，支配的稳态相似性解决方案适用于描述致密颗粒介质的任何摩擦定律。这些稳态解决方案体现了沿倾斜斜槽顺着稠密颗粒流动的关键方面，在各种工业应用中得到了广泛的应用，并将进一步帮助对自然地球物理现象进行建模。我们为某些特殊情况提供稳态分析解决方案，并且我们强调相似性解决方案作为涉及致密颗粒流的复杂材料行为的各种数值研究的基准标准的重要性。